First slide

Differentiability

Question

$Let f (x + y) = f (x) f (y) and f (x) = 1 + (\sin 2 x) g (x) where g (x) is continues.$ $Then f^{1} (x) equals$

Moderate

A

$f (x) g (0)$
B

$2 f (x) g (0)$
C

$2 g (0)$
D

$2 f (0)$

Solution

$\begin{array}{l} f' (x) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h} = lim_{h \to 0} \frac{f (x) f (h) - f (x)}{h} \\ = f (x) lim_{h \to 0} \frac{f (h) - 1}{h} = f (x) lim_{h \to 0} \frac{1 + (\sin 2 h) g (h) - 1}{h} \\ = f (x) lim_{h \to 0} \frac{\sin 2 h}{h} lim_{h \to 0} (h) = 2 f (x) g (0) \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App